<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2022000400013</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.68.041301</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Light refraction in the earth&#8217;s atmosphere I. Inferior mirages: analytic solution of ray paths]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Paola]]></surname>
<given-names><![CDATA[C. Alejandro]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cruzado]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Carrasco Galleguillos]]></surname>
<given-names><![CDATA[F. M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Univesidad Nacional de La Plata Facultad de Ciencias Astronómicas y Geofísicas ]]></institution>
<addr-line><![CDATA[La Plata Buenos Aires]]></addr-line>
<country>Argentina</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Univesidad Nacional de La Plata Facultad de Ciencias Astronómicas y Geofísicas ]]></institution>
<addr-line><![CDATA[La Plata Buenos Aires]]></addr-line>
<country>Argentina</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Univesidad Nacional de La Plata Facultad de Ciencias Astronómicas y Geofísicas ]]></institution>
<addr-line><![CDATA[La Plata Buenos Aires]]></addr-line>
<country>Argentina</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>08</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>08</month>
<year>2022</year>
</pub-date>
<volume>68</volume>
<numero>4</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2022000400013&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2022000400013&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2022000400013&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We aim to reach an analytic expression that describes the path of light rays through the Earth&#8217;s atmosphere in the particular situation in which an inferior mirage is occurring. To achieve our goal, we assume an exponential refractive index profile close to the ground, as suggested by empirical and theoretical studies on the state of air when an inferior mirage is taking place. We consider a parallel-plane atmosphere and assume that the laws of geometric optics apply. Since Fermat&#8217;s principle holds, we solve the Euler&#8217;s equation and, from the solution we obtain an analytic expression that describes the ray paths in a plane perpendicular to the ground. Given that we focus on the particular case of inferior mirages, we were able to find a very simple and easy-to-use expression to describe the ray paths, allowing us to extract additional valuable information with minimal computational effort. We take advantage of it to impose a limit to the thickness of the air layer next to the ground where appropriate conditions exist to bend the rays upwards, and produce an inferior mirage.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Planetary atmospheres]]></kwd>
<kwd lng="en"><![CDATA[light refraction]]></kwd>
<kwd lng="en"><![CDATA[inferior mirages]]></kwd>
<kwd lng="en"><![CDATA[analytic expression]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Danjon]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Astronomie generale. Astronomie spherique et elements de mecanique celeste]]></source>
<year>1959</year>
<edition>2</edition>
<page-range>143</page-range><publisher-loc><![CDATA[Paris ]]></publisher-loc>
<publisher-name><![CDATA[J. &amp; R. Sennac editeurs]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mahan]]></surname>
<given-names><![CDATA[A. I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Astronomical refraction, some history and theories]]></article-title>
<source><![CDATA[Appl. Opt.]]></source>
<year>1962</year>
<volume>1</volume>
<page-range>497</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Garfinkel]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Astronomical refraction in a polytrophic atmosphere]]></article-title>
<source><![CDATA[Astron. J.]]></source>
<year>1967</year>
<volume>72</volume>
<page-range>235</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yatsenko]]></surname>
<given-names><![CDATA[A. Yu]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Exact theory of astronomical refraction for the real atmosphere]]></article-title>
<source><![CDATA[A&amp;AS]]></source>
<year>1995</year>
<volume>111</volume>
<page-range>579</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Young]]></surname>
<given-names><![CDATA[A. T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Understanding astronomical refraction]]></article-title>
<source><![CDATA[The Observatory]]></source>
<year>2006</year>
<volume>126</volume>
<page-range>82</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Corbard]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Ikhlef]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Morand]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Meftah]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Renaud]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the importance of astronomical refraction for modern solar astrometric measurements]]></article-title>
<source><![CDATA[MNRAS]]></source>
<year>2019</year>
<volume>483</volume>
<page-range>3865</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Evans]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosenquist]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[F = ma optics]]></article-title>
<source><![CDATA[Am. J. Phys.]]></source>
<year>1985</year>
<volume>54</volume>
<page-range>876</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Evans]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Simple forms for equations of rays in gradient-index lenses]]></article-title>
<source><![CDATA[Am. J. Phys.]]></source>
<year>1980</year>
<volume>58</volume>
<page-range>773</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nener]]></surname>
<given-names><![CDATA[B. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Fowkes]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Borredon]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Analytical models of optical refraction in the troposphere]]></article-title>
<source><![CDATA[J. Opt. Soc. Am. A.]]></source>
<year>2003</year>
<volume>20</volume>
<page-range>867</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fowkes]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Nener]]></surname>
<given-names><![CDATA[B. D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Microwave propagation over the Earth: image inversion]]></article-title>
<source><![CDATA[Journal of Engineering Mathematics]]></source>
<year>2005</year>
<volume>53</volume>
<page-range>253</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Berger]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Trout]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Levit]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ray Tracing Mirages]]></article-title>
<source><![CDATA[IEEE Computer Graphics and Applications]]></source>
<year>1990</year>
<volume>10</volume>
<page-range>36</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Musgrave]]></surname>
<given-names><![CDATA[F. K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Note on Ray Tracing Mirages]]></article-title>
<source><![CDATA[IEEE Computer Graphics and Applications]]></source>
<year>1990</year>
<volume>10</volume>
<page-range>10</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stam]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Languenou]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ray Tracing in Non-Constant Media]]></article-title>
<source><![CDATA[In Proc. Eurographics Workshop on Rendering]]></source>
<year>1996</year>
<page-range>225</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gutierrez]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Seron]]></surname>
<given-names><![CDATA[F. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Munoz]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Anson]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Simulation of atmospheric phenomena]]></article-title>
<source><![CDATA[Computers &amp; Graphics]]></source>
<year>2006</year>
<volume>30</volume>
<page-range>994</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Born]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wolf]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Principles of Optics]]></source>
<year>1959</year>
<publisher-name><![CDATA[Pergamon Pres]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jackson]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Classical Electrodynamics]]></source>
<year>1975</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Wiley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stull]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[An Introduction to Boundary Layer Meteorology]]></source>
<year>1988</year>
<publisher-loc><![CDATA[Dordrecht ]]></publisher-loc>
<publisher-name><![CDATA[Kluwer Academic PUblishers]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kannuluik]]></surname>
<given-names><![CDATA[W. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Carman]]></surname>
<given-names><![CDATA[E. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Temperature Dependence of the Thermal Conductivity of Air]]></article-title>
<source><![CDATA[Australian J. Sci. Res.]]></source>
<year>1951</year>
<volume>4</volume>
<page-range>305</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>19</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ciddor]]></surname>
<given-names><![CDATA[P. E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Refractive index of air: new equations for the visible and near infrared]]></article-title>
<source><![CDATA[Applied Optics]]></source>
<year>1996</year>
<volume>35</volume>
</nlm-citation>
</ref>
<ref id="B20">
<label>20</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Garrat]]></surname>
<given-names><![CDATA[J. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Extreme Maximun Land Surface Temperatures]]></article-title>
<source><![CDATA[Journal of Applied Meteorology]]></source>
<year>1991</year>
<volume>31</volume>
<page-range>1096</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>21</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heusinkveld]]></surname>
<given-names><![CDATA[B. G.]]></given-names>
</name>
</person-group>
<source><![CDATA[On dew and micrometeorology in an arid coastal ecosystem]]></source>
<year>2008</year>
<publisher-loc><![CDATA[Wageningen University and Research ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B22">
<label>22</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pfeiffer]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Soil Temperature and Relative Humidity at the Yungay Hiperarid site, Atacama Desert, Chile 2015-2017]]></source>
<year>2021</year>
<publisher-name><![CDATA[PANGAEA, Data Publisher for Earth &amp; Environmental Science]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
